Illumination systems to illuminate a specified illumination field of an object surface with EUV radiation are disclosed in U.S. Pat. No. 6,859,328 B2, U.S. 2005/0093041 A1, U.S. Pat. No. 6,858,853 B2, U.S. 2005/0002090 A1, U.S. 2003/0095623 A1, U.S. Pat. No. 6,400,794 B1 and WO 01/065482 A. A collector to concentrate EUV radiation is disclosed in DE 100 45 265 A1. The illumination systems are part of a projection exposure system, and are used in micro-lithography for producing integrated circuits, to illuminate an object in the form of a mask or reticle.